15‏/11‏/2009

Delta, gamma, risk reversals and volatility are concepts familiar to nearly all options traders. However, these same tools used to trade currency options can also be useful in predicting movements in the underlying, which in foreign exchange (FX) is the cash or spot product. In this article, we look at how volatility can be used to determine upcoming market activity, how delta can be used to calculate the probability of spot movements, how gamma can predict trading environments and how risk reversals are applicable to the cash market.

Using Volatility to Forecast Market ActivityOption volatilities measure the rate and magnitude of the changes in a currency's price. Implied option volatilities on the other hand measure the expected fluctuation of a currency’s price over a given period of time based upon historical fluctuations. Volatility calculations typically involve the historic annual standard deviation of daily price changes.

In using volatility to forecast market activity, the trader needs to make certain comparisons. Although the most reliable comparison is implied versus actual, the availability of actual data is limited. Alternatively, comparing historical implied volatilities are also effective. One-month and three-month implied volatilities are two of the most commonly benchmarked time frames used for comparison (the numbers below represent percentages).Source: IFR Market News Plug-in

Typically in range-trading scenarios, implied option volatilities are low or declining because in periods of range trading, there tends to be minimal movement. When option volatilities take a sharp dive, it can be a good signal for an upcoming trading opportunity. This is very important for both range and breakout traders. Traders who usually sell at the top of the range and buy at bottom, can use option volatilities to predict when their strategy might stop working - more specifically, if volatility contracts become very low, the likelihood of continued range trading decreases.

Breakout traders, on the other hand, can also monitor option volatilities to make sure that they are not buying or selling into a false breakout. If volatility is at average levels, the likelihood of a false breakout increases. Alternatively, if volatility is very low, the probability of a real breakout increases. These guidelines generally work well, but traders also have to be careful. Volatilities can have long downward trends (as they did between June and Oct 2002) during which time volatilities can be misleading. Traders need to look for sharp movements in volatilities, not a gradual one.

The following is a chart of USD/JPY. The green line represents short-term volatility, the red line long-term volatility and the blue line price action. The arrows with no labels are pointing to periods when short-term volatility rises significantly above long-term volatility. You can see such divergence in volatility tends to be followed by periods of range trading. The ‘1M implied’ arrow is pointing to a period when short-term volatility dips below long-term volatility. At price action above that, a breakout occurs when short-term volatility reverts back towards long-term volatility. Using Delta to Calculate Spot ProbabilitiesWhat Is Delta?Options price can be seen as a representation of the market’s expectation of the future distribution of spot prices. The delta of an option can be thought of roughly as the probability of the option finishing in the money. For example, given a one-month USD/JPY call option struck at 104 with a delta of 50, the probability of USD/JPY finishing above 104 one month from now would be approximately 50%.

Calculating Spot ProbabilitiesWith information on deltas, one can approximate the market’s expectation of the likelihood of different spot levels over time. When the probability of the spot finishing above a certain level, call-option deltas are used. Similarly when the probability of spot finishing below a certain level, put-option deltas are used.

The key to calculating expected spot levels is using conditional probability. Given two events, A and B, the probability of A and B occurring is calculated as follows:

P(A and B) = P(A)*P(B|A)

In words, the probability of A and B occurring is equal to the probability of A times the probability of B given the occurrence of A.Here is the formula applied to the problem of calculating the probability that spot will touch a certain level:

In words, the probability of spot touching and finishing above a certain level (or delta) is equal to the probability of spot touching that level times the probability of spot finishing above a certain level given that is has already touched that level.Given options prices and corresponding deltas, this probability calculation can be used to get a general idea of the market’s expectations of various spot levels. The rule-of-thumb this methodology yields is that the probability of spot touching a certain level is roughly equivalent to two times the delta of an option struck at that level.

Using Gamma to Predict Trading EnvironmentsWhat Is Gamma?Gamma represents the change in delta for a given change in the spot rate. In trading terms, players become long gamma when they buy standard puts or calls, and short gamma when they sell them. When commentators speak of the entire market being long or short gamma, they are usually referring to market makers in the interbank market.

How Market Makers View GammaGenerally, options market makers seek to be delta neutral - that is, they want to hedge their portfolios against movement in the underlying spot rate. The amount by which their delta, or hedge ratio, changes is known as gamma.

Say a trader is long gamma, meaning he or she has bought some standard vanilla options. Assume they are USD/JPY options. If we further assume that the delta position of these options is $10 million at USD/JPY 107, the trader will need to sell $10 million USD/JPY at 107 in order to be fully insulated against spot movement.

If USD/JPY rises to 108, the trader will need to sell another $10 million, this time at 108, as the total delta position becomes $20 million. What happens if USD/JPY goes back to 107? The delta position goes back to $10 million, as before. Because the trader is now short $20 million, he or she will need to buy back $10 million at 107. The net effect then is a 100-pip profit, selling a 108 and buying at 107.

In sum, when traders are long gamma, they are continually buying low and selling high, or vice versa, in order to hedge. When the spot market is very volatile, traders earn a lot of profits through their hedging activity. But these profits are not free, as there is a premium to own the options. In theory, the amount you make from delta hedging should exactly offset the premium. Whether or not this is true in practice depends on the actual volatility of the spot rate.

The reverse is true when a trader has sold options. When short gamma, in order to hedge, the trader must continually buy high and sell low - thus he or she loses money on the hedges, in theory the exact same amount earned in options premium through the sales.

Why Is Gamma Important for Spot Traders?But what relevance does all this have for regular spot traders? The answer is that spot movement is increasingly driven by what goes on in the options market. When the market is long gamma, market makers as a whole will be buying spot when it falls and selling spot when the exchange rate rises. This behavior can generally keep the spot rate in a relatively tight range.

When the market is short gamma, however, the spot rate can be prone to wide swings as players are either continually selling when prices fall, or buying when prices rise. A market that is short gamma will exacerbate price movement through its hedging activity. Thus:

* When market makers are long gamma, spot generally trades in a tighter range. * When market makers are short gamma, spot can be prone to wide swings.

Using Risk Reversals to Judge Market PositioningWhat Are Risk Reversals?Risk reversals are a representation of the market’s expectations on the exchange-rate direction. Filtered properly, risk reversals can generate profitable overbought and oversold signals.

A risk reversal consists of a pair of options, a call and a put, on the same currency, with the same expiration (one month) and sensitivity to the underlying spot rate. Risk reversals are quoted in terms of the difference in volatility between the two options. While in theory these options should have the same implied volatility, in practice they often differ in the market. A positive number indicates that calls are preferred to puts and that the market is expecting a move up in the underlying currency. Likewise, a negative number indicates that puts are preferred to calls and that the market is expecting a move down in the underlying currency.

Risk reversals can be seen as having a ‘market polling function’. A positive risk-reversal number implies that more market participants are voting for a rise in the currency than for a drop. Thus, risk reversals can be used as a substitute for gauging positions in the FX market.

How Can Risk Reversals Be Used to Predict Spot-Currency Movement?While the signals generated by a risk-reversal system will not be completely accurate, they can specify when the market is bullish or bearish.

Risk reversals convey the most information when they are at relatively extreme values. These extreme values are commonly defined as one standard deviation beyond the averages of positive and negative values. Therefore we are looking at values one standard deviation below the average of negative risk-reversal figures, and values one standard deviation above the average of positive risk-reversal figures.

When risk reversals are at these extreme values, they give off contrarian signals - when the entire market is positioned for a rise in a given currency, it makes it that much harder for the currency to rally, and that much easier for it to fall on negative news or events. A large positive risk-reversal number implies an overbought situation, while a large negative risk-reversal number implies an oversold situation. The buy or sell signals produced by risk reversals are not perfect, but they can convey additional information used to make trading decisions.

SummaryThere are many tools used by seasoned options traders that can also be useful to trading spot FX. Volatility can be used to forecast market activity in the cash component through comparing short-term versus longer term implied volatilities. Delta can help estimate the probability of the spot rate reaching a certain level. And gamma can predict whether spot will trade in a tighter range if it is vulnerable to wider swings. Risk reversals are a representation of the market's expectations on exchange-rate direction. If filtered properly, risk reversals can be used to gauge market sentiment and determine overbought and oversold conditions.